What Is the Smallest Thing You Would Still Call a Hill?

Start with something that is obviously a hill and take a metre off the top. It is still a hill. Take another metre. Still a hill. Keep going, one metre at a time, and at no single step does it clearly stop being one. And yet, if you carry on long enough, you end up standing in front of a slight rise in a field that nobody would ever dignify with the word. Somewhere along the way the hill vanished, but there is no moment you can point to and say: there, that was it.

You might hope that geographers have settled the matter with a rule. They have not. According to National Geographic Education, a hill is a piece of land that rises higher than everything surrounding it, and hills are generally easier to climb than mountains because they are less steep and not as high. But the same source is clear that there is no official difference between hills and mountains, let alone an official minimum height for a hill.

There once was an attempt at a rule. National Geographic Education reports that the United Kingdom and the United States used to define hills as summits less than 1,000 feet high. Both countries, it says, abandoned that distinction in the mid-twentieth century. So even the neat, measurable boundary that people once tried to draw did not survive, and today the word hill is left to do its job without any number attached to it.

Philosophers have a name for exactly this puzzle. The Stanford Encyclopedia of Philosophy describes the sorites paradox, which takes its name from the Greek word soros, meaning heap, and is credited to the ancient philosopher Eubulides in the fourth century BC. The classic version asks about grains of sand: no single grain can make the difference between a heap and not a heap, and yet by adding or removing grains one at a time you seem forced into absurd conclusions.

The encyclopedia explains that the paradox arises from vague terms, words with blurred or fuzzy boundaries, such as bald, tall, old and blue. For words like these there is no clear line dividing the things that fit from the things that do not. Hill belongs comfortably in the same family. The difficulty is not that we have failed to measure hills carefully enough. It is that the word itself was never built with a sharp edge.

So what is the smallest thing you would still call a hill? The honest answer is that it depends on you, the landscape and perhaps your legs. A modest rise in very flat country may feel like a proper hill, while a bump of the same height halfway up a mountain may go unnamed. The word works perfectly well in everyday life precisely because it does not need a precise boundary. You simply know one when you are standing at the bottom of it.